\subsection{Problem 5}
Find $\mathbf{A^{-1}}$ to:

\begin{equation*}
    \matr{A} = 
    \begin{bmatrix}
        2 & 1 & 2 \\
        1 & 2 & 3 \\
        4 & 1 & 2 
    \end{bmatrix}
\end{equation*}

solving the system $\mathbf{AX=I_{3}}$.

\subsubsection*{Solution}
\lstinputlisting[style=Matlab-editor]{problems/Problem5.m}
which judges well our algorithms.